Is the 64-Bit version of Ubuntu only compatible with AMD CPUs?

There is a slight misunderstanding here. AMD64 refers to the architecture of the processor. As AMD's X86-64 extension prevailed in the "64-Bit format war", it is named after them; just like people used to call all PCs IBM-PC-compatible.

The gist of the matter is: You can install AMD64 software on both AMD and Intel processors, as long as they support that type of architecture (Don't worry, almost all processors released in the last 5 years do). So just go ahead and install Ubuntu using the 64 bit iso.

Finally, if your CPU has PAE enabled, you can access more than the limited "4G" of RAM using 32-bit processors.

See also:

• What are the differences between 32-bit and 64-bit, and which should I choose?
• Difference between the i386 download and the amd64?

Intel uses the same 64-bit instruction set as AMD. 64-bit Ubuntu will work fine.

The 64-bit instruction set currently used in desktop computers was invented by AMD, which is why it's sometimes referred to as "amd64", even though it is used by both AMD and Intel processors.

A less confusing name for the same instruction set is "x86-64", reflecting the fact that it's 64-bit extension to the original x86 instruction set.

Years ago, Intel developed an alternative 64-bit instruction set call IA-64 (brand name "Itanium") but it was never successful in the consumer market, and they have since standardised on the same set as AMD.